Surfactant-based monolithic columns, methods for making the same, and method for using the same

ABSTRACT

A method for making a surfactant-based monolithic column is provided. The method comprises providing a mixture comprising at least one surfactant monomer, at least one crosslinker, at least one initiator, and at least one porogen and polymerizing the mixture to form the surfactant-based monolithic column. The present disclosure also provides a surfactant-based monolithic column, a method for separating molecules, and a process for preparing a surfactant monomer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a submission pursuant to 35 U.S.C. 154(d)(4) to enter thenational stage under 35 U.S.C. 371 for PCT/US09/38756, filed Mar. 30,2009. Priority is claimed under 35 U.S.C. 119(e) to U.S. ProvisionalPatent Application No. 61/041,267, filed Apr. 1, 2008. The subjectmatters of international application no. PCT/US09/38756 and U.S.Provisional Patent Application No. 61/041,267 expressly are incorporatedherein by reference in their entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with U.S. government support under Grant No.1R01-GM-062314 awarded by the National Institutes of Health. The U.S.government has certain rights in the invention.

FIELD OF INVENTION

The invention generally relates to monolithic polymeric columns forchromatography.

BACKGROUND OF THE INVENTION

The current use of particle-based packed chromatography columns involvespacking particles dissolved in a slurry into a tube and then burningfrits on either end of the packed tube to retain the packed bed in thetube. This procedure is more of an art than a science and requiresskilled personnel to pack the tubes and burn the frits. Thus, manuallypacked particle-based chromatography columns have significantperson-to-person reproducibility issues.

In addition, particle-based packed columns for use in capillaryelectrochromatography (CEC) are time consuming to fabricate, fragile,and tend to have bubble formation. The bubble formation causesirreproducible retention times and peak areas, therefore makingparticle-based packed columns impractical to use for the analysis ofreal world samples.

Polymeric monolithic stationary phases offer an alternative to theclassical microparticulate sorbents and provide certain advantages forsample analysis. In contrast to the traditional packed particlestationary phases, monolithic separation media are made of a continuous,rigid polymeric rod with a porous structure. The lack of intraparticularvoid volume improves mass transfer and separation efficiency, allowingfor fast, high-quality separations.

For almost a decade, CEC using monolithic columns has been a growingfield of research as an alternative to the traditional packed columnCEC. The main advantages of monolithic columns for CEC are: theuncomplicated procedures for column preparation, the flexibility intuning the columns' pore structure, the elimination of the need forfrits, the availability of various functional monomers in the columnsfor selective separation, and the exclusion or reduction of bubbleformation during operation. Hence, use of monolithic column technologyhas increased and new stationary phases and column-preparationmechanisms are being researched. Furthermore, a large number of new andattractive applications have been developed in biological,environmental, and pharmaceutical analysis which may benefit from usingmonolithic column technology.

The stationary phase used for CEC plays a dual role of providing sitesfor the desired interaction with analytes and sites for generatingelectroosmotic flow (EOF). For instance, in the preparation of amethacrylate-based monolith used for CEC, a charge-bearing monomer, suchas 2-acrylamido-2-methyl-1-propanesulfonic acid, is often used toprovide stable EOF in addition to use of a functional monomer. There isa need for monolithic columns that are chargeable and thus suitable forCEC. There is furthermore a need for monolithic chromatography columnswith enhanced electro-osmotic flow.

The advantages of capillary high performance liquid chromatography(HPLC) over conventional normal scale HPLC also have been recognized.Those advantages include increased chromatographic resolution, lowersample consumption, the ability to analyze and isolate rare compounds ofinterest, reduced solvent consumption and convenient on-line connectionto electrospray mass spectrometry.

It would be desirable to provide additional monolithic columns forchromatography, such ac CEC and HPLC, which reduce or avoid one or morethe aforementioned deficiencies.

SUMMARY OF THE INVENTION

The present disclosure provides a method for making a surfactant-basedmonolithic column. The method comprises providing a mixture comprisingat least one surfactant monomer, at least one crosslinker, at least oneinitiator, and at least one porogen and polymerizing the mixture to formthe surfactant-based monolithic column.

The present disclosure also provides a surfactant-based monolithiccolumn comprising a surfactant-based polymer monolith.

The present disclosure additionally provides a method for separatingmolecules comprising providing surfactant-based monolithic column,providing a mixture of the molecules and a mobile phase, and passing themixture through the surfactant-based monolithic column.

The present disclosure further provides a process for preparing11-acrylamidoundecanoic acid polymer, the process comprising providing acarboxylic acid having a 6 to 20 carbon chain length and a tail group,wherein the tail group comprises NH₂, or OH; reacting the carboxylicacid with aryloyl chloride to form a first product; reacting the firstproduct with 1-hydroxypyrrolidine-2,5-dione to form a second product;and reacting the second product with an amino acid to form a surfactantmonomer including an amino acid functional group.

Other objects, features, and advantages of this invention will beapparent from the following detailed description, drawings, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the disclosure can be better understood with referenceto the following figures. Please see the text and examples for furtherdescription of the figures.

FIG. 1 shows electrochromatograms for separation of thiourea andalkylbenzenes (A1, B1) and thiourea and alkyl phenyl ketones (A2, B2)for two embodiments of the present invention (columns 7 and column 1 asdescribed in Example 1).

FIG. 2 shows regression coefficients plots for alkylbenzenes separationperformances for embodiments of the present invention.

FIG. 3 shows regression coefficients plots for alkyl phenyl ketonesseparation performances for embodiments of the present invention.

FIG. 4 shows contour plots obtained for average efficiency (N_(avg)),average resolution (Rs_((avg))) and the total analysis time (Rt) ofalkylbenzenes as a function of concentrations of components in apolymerization mixture according to embodiments of the presentinvention.

FIG. 5 is a graph displaying the pore size distribution of threeembodiments of the present invention.

FIG. 6 is a graph displaying the measured pressure drop against mobilephase flow rate as measured with three embodiments of the presentinvention.

FIG. 7 shows plots of logarithmic retention factor (log k′) ofalkylbenzenes and alkyl phenyl ketones versus % acetonitrile (v/v) inthe mobile phase for embodiments of the present invention.

FIG. 8 is a Van Deemter plot showing average plate height as a functionof apparent mobile-phase flow velocity for thiourea, alkylbenzenes andalkyl phenyl ketones on one embodiment of the present invention.

FIG. 9 is a plot of CEC separation of N-methylcarbamates (NMCs)pesticides obtained on one embodiment of the present invention.

FIG. 10 shows chromatograms for separation of proteins on twoembodiments of the present invention.

FIGS. 11A-C are regression coefficients plots for proteins separationperformances for embodiments of the present invention.

FIGS. 12A-C are contour plots and obtained for average efficiency(Navg), average resolution (Rs (avg)) and the total analysis time (Rt)of proteins as a function of as a function of concentrations ofcomponents in a polymerization mixture according to embodiments of thepresent invention.

FIG. 13 is a graph displaying the pore size distribution of threeembodiments of the present invention (columns 7, 10/OH-1, and OF-1 asdescribed in Example 2).

FIG. 14 is a chromatogram of separation of proteins using twoembodiments of the present invention.

FIG. 15 is a graph displaying the pore size distribution of threeembodiments of the present invention.

FIG. 16 is a graph displaying the measured pressure drop against mobilephase flow rate as measured with three embodiments of the presentinvention (Columns 7, 10/OH-1, and OF-1 as described in Example 2).

FIG. 17 shows Van Deemter plots showing average plate height of proteinsas a function of mobile-phase flow velocity according to two embodimentsof the present invention (a: OH-1; b: OF-1).

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As summarized above, this disclosure encompasses a method making asurfactant-based monolithic column, a surfactant-based monolithiccolumn, a method for separating a plurality of molecules, and a processfor preparing a surfactant monomer. As used herein, the terms “monolith”and “monolithic” include a porous, three-dimensional materials having acontinuous interconnected pore structure, as distinguished from acollection of individual particles. As used herein the term “column”refers to any three-dimensional material having a shape, such as acylindrical shape, a disk shape, a chip shape, an elongated shape (e.g.,a capillary shape having a polygonal cross-section), or any other shapewhich is suitable for a mobile phase to travel through at least aportion of the column. Unless otherwise indicated, all % units are in %(weight/weight).

In particular embodiments, the surfactant-based monolithic columns aremade from polymerizable surfactant monomers, which are polymerizedin-situ in a tube or column with at least one crosslinker, at least oneinitiator, and at least one porogen.

In one embodiment, the method for making a surfactant-based monolithiccolumn comprises (a) preparing a solution of surfactant monomer with ahydrocarbon chain having a carbon length ranging from about 6 to about20, (b) introducing at least one crosslinker, at least one initiator,and at least one porogen, and (c) polymerizing and coalescing thematerials (i.e., the polymerization mixture) in a tube or column.

Embodiments of the surfactant monomer have surfactant properties. Incertain embodiments, the surfactant monomers comprise a carbon chainhaving length of about 6 to about 20 carbons with a functionalized headgroup, such as carboxylic acid (—COOH), an amino acid group, sufonate,sulfate, ammonium, or phosphonium, and a conjugated tail group, such asacrylamide or acrylate. In one embodiment, the surfactant monomercomprises a 6 to 18 carbon chain. In some embodiments, the monomer mayhave a chain length shorter than 6, but may be difficult to purify. Inother embodiments, the polymerizable surfactant monomers may have achain length longer than 20, but solubility of the monomer may bereduced. By using surfactant monomers, longer hydrocarbon monomers thatare hydrophobic with a charge-bearing group, separate charge-bearingmolecules (i.e., charging molecules or chargeable molecules) do not needto be added to the polymerization mixture. Thus, certain embodiments ofthe surfactant monomers are considered “mixed-mode” becausechromatographic retention of the polymers made from such monomers isprovided by the hydrophobic portion (e.g., the long carbon chain) andEOF is provided by the charge-bearing molecule.

Suitable surfactant monomers for use in embodiments of the presentdisclosure include, but are not limited to, 11-acrylamidoundecanoic acid(AAUA), 6-acrylamido-hexanoic acid, 7-acrylamido-heptanoic acid,17-acrylamido-hepatadecanoic acid, 18-acrylamido-octadecanoic acid,19-acrylamido-nonadecanoic acid, 20-acrylamido-eicosanoic acid, or acombination thereof. In one embodiment, the surfactant monomers arechiral monomers. In particular embodiments, the surfactant monomer ispresent in the polymerization mixture in an amount ranging from about0.5% (w/w) to about 7% (w/w).

The at least one crosslinker may include any suitable crosslinkereffective to crosslink the monomer used, including commerciallyavailable crosslinkers. Examples of suitable crosslinkers include, butare not limited to, ethylene dimethacrylate (EDMA), pentaerythritoldiacrylate monostearate (PEDAS), divinylbenzene, piperazine diacrylamide(PDA), polyethyleneglycol diacrylate (PEGDA),N,N′-methylenebisacrylarnide, N,N′-diallayl L-tartardiamide,N,N′-diallayl-tartardiamide or a combination thereof. In someembodiments, the crosslinker may be a commercially availablecrosslinker. In particular embodiments, the crosslinker is present inthe polymerization mixture in an amount ranging from about 18.5% (w/w)to about 21.3% (w/w).

The at least one initiator may include known initiators effective ininitiating a polymerization of the selected polymerizable surfactantmonomer. Examples of suitable initiators include, but are not limitedto, azoisobutyronitrile (AIB or AIBN), ammonium peroxodisulfate(APS)/tetramethylenediamine (TEMED), or a combination thereof. In someembodiments, the initiator may be a commercially available initiator. Inalternate embodiments, photopolymerization using UV-radiation (530 nm)and ⁶⁰C0 γ-radiation sources can also be used to initiate thepolymerization. In particular embodiments, the initiator is present inthe polymerization mixture in an amount ranging from about 0.1% (w/w) toabout 1% (w/w).

At least one porogen may also be used to regulate the pore structure(e.g., control pore size) in the polymerization of the monolith.Suitable porogens include, but are not limited to, 1-propanol,1,4-butanediol, water, acetonitrile, methanol, dodecanol, decanol,cyclohexanol, dimethyl sulfoxide, N,N-dimethylformamide, or acombination thereof.

The concentration of and ratios of the porogens may be modified to reachthe desired pore structure. In particular embodiments, the porogen maycomprise water, which is present in the polymerization mixture in anamount ranging from about 2% (w/w) to about 12% (w/w), 1,4-butanediol,which is present in the polymerization mixture in an amount ranging fromabout 0% (w/w) to about 12% (w/w), and 1-propanol, which is present inthe polymerization mixture in an amount ranging from about 60% (w/w) toabout 74% (w/w).

In other embodiments, the surfactant monomers may be copolymerized witha copolymer monomer using the at least one crosslinker, at least oneinitiator, and at least one porogen. Suitable copolymer monomers for usein embodiments of the present disclosure include, but are not limitedto, methyl methacrylate, butyl-methacrylate, methacrylate, glycerylmethacrylate, butylaclylamide, methacrylamide, N,N-dimethylacrylamide,or combinations thereof.

In one embodiment of the method for forming the monolith, the monomerand other components are polymerized in situ in a commercially availablecapillary tube or column. The tube and in situ materials are maintainedat a polymerization temperature for a period of time while thepolymerization occurs. In some embodiments, the polymerizationtemperature is higher than room temperature. In other embodiments, thepolymerization temperature ranges from about 45° C. to about 70° C. Instill other embodiments, the polymerization temperature is about 60° C.The polymerization temperature is maintained long enough to allowcomplete or almost complete polymerization and crosslinking. Thus, inparticular embodiments, the polymerization temperature is maintained formore than about 10 hours. In other embodiments, the polymerizationtemperature is maintained for more than 15 hours. In still otherembodiments, the polymerization temperature is maintained for about 20hours.

In certain embodiments, the polymerization may be carried out onvinylized (i.e., silanized) capillaries. For example, capillaries may bevinylized with 3-(trimethoxylsilyl)propyl methacrylate beforepolymerization of a surfactant monomer in the capillary so as to providevinyl groups for further polymerization. Since the3-(trimethoxylsilyl)propyl methacrylate contains hydroxyl groups, itwill attack and displace the alkoxy groups on silane to form a covalent—Si—O—Si— bond (i.e., silanization).

In one embodiment, the polymerizable surfactant monomer is AAUA, whichis synthesized from 11-aminoundecanoic acid and acryloyl chloride in thepresence of aqueous ethanol and a sodium hydroxide (NaOH) buffer as seenin Scheme 1. As shown, the synthesized AAUA monomer has a C₁₁ longhydrocarbon chain to provide hydrophobic interaction, the acrylamidoterminated polymerizable group, and a carboxyl group providingchargeable site to produce EOF. This kind of monolith is beneficialbecause it eliminates the need of introducing ionizable monomers inaddition to the functional monomer. As also show in Scheme 1, EDMA isintroduced as a crosslinker and AIBN is used as the initiator. The porestructure of the polymerizing polymer is controlled by adding porogenscomprising 1-propanol, 1,4-butanediol, and water during the coalescingphase.

As seen in Scheme 1, the monomer and other components coalesce into aporous polymer by maintaining an elevated temperature of 60° C. overabout 20 hours. A crosslinked surfactant-based polymer (i.e.,poly(AAUA-co-EDMA)) is therefore produced. Concentration ranges for thecomponents of the polymerization mixture used in embodiments of thereactions provided in Scheme 1 are provided in Table 1.

TABLE 1 Levels Components¹ Lower limit (−1) Upper limit (+1) A: EDMA18.5% 21.3% B: AAUA 1.8% 7.0% C: 1-propanol 60.0% 74.0% D:1,4-butanediol 0 12.0% E: Water 2.0% 12.0% ¹A + B + C + D + E = 99.5%

Another embodiment of the method for making a surfactant-basedmonolithic column is synthesized using a monomer including an amino acidfunctional group as seen in Scheme 2A-B. In this embodiment, a porouspolymer may be produced by synthesizing a solution of monomer with anappropriate leaving group by starting from a 6 to 20 carbon carboxylicacid with an OH tail and reacting it with aryloyl chloride and then1-hydroxypyrrolidine-2,5-dione by the reactions seen in Scheme 2A-B,where TEA is triethylamine and DCC is dicyclohexylcarbodiimide. Themethod further includes introducing a functional group selected from anyof the amino acids (R) in a buffered solution of tetrahydrofuran (THF)and water to produce a surfactant monomer with a desirable selectivitytraits, introducing a crosslinker, EDMA, and initiator, AIBN, modifyingthe pore structure of the porous material by varying the concentrationof porogens, such as 1-propanol, 1,4-butanediol, and water, present insolution during the coalescing phase, and coalescing the componentmaterials into a polymerized monolith column by means of elevatedtemperature over an extended period of time.

Without being bound by a particular theory, it is believed that the poresize and selectivity of the resultant monolithic column can becontrolled by varying the concentrations and identities of the at leastone crosslinker, at least one initiator, and the at least one porogenand the concentrations and chain length of the surfactant monomer. Inparticular embodiments, the chromatographic selectivity of the resultantchromatographic surfactant-based monolithic column may be controlled byintroducing a particular amino acid functional group suitable toprovided the desired selectivity.

Another embodiment of the invention as depicted in Scheme 3A-B allowsthe chromatographic selectivity of the resultant chromatographicsurfactant-based monolithic column to be controlled. This monolith isproduced by (a) synthesizing a solution of a monomer with an appropriateleaving group, starting from a 6 to 20 carbon carboxylic acid with a NH₂tail and reacting it with aryloyl chloride and then1-hydroxypyrrolidine-2,5-dione by the reactions seen in Scheme 3A-B,where TEA is triethylamine, EtOH is ethanol, NaOH is sodium hydroxide,and DCC is dicyclohexylcarbodiimide, (b) introducing a functional groupselected from an amino acid, such as the amino acids (R) in Scheme 2, ina buffered solution of tetrahydrofuran (THF) and water to produce asurfactant monomer with particular selectivity traits; (c) introducing acrosslinker, such as EDMA and at least one initiator, such as AIBN; (d)modifying the pore structure of the porous material by varying theconcentration of porogens, such as 1-propanol, 1,4-butanediol, water;and (e) coalescing the component materials into a polymerized monolithcolumn by means of elevated temperature over a period of time.

Thus, embodiments of the surfactant-based monolithic column made frommethods described include a surfactant-based polymer.

Monolithic columns produced according to embodiments of the presentinvention may be used in a variety of analytical separations. In someembodiments, the surfactant-based monolithic column is a part of aseparation device. For example, the columns according to the inventioncan be used for HPLC processes, including nano-HPLC and micro-HPLC, CEC,gas chromatography (GC), and/or supercritical fluid chromatography(SFC). In one embodiment, the surfactant-based monolithic columncomprises an anionic surfactant-based monolithic stationary phase foruse in CEC.

Columns made from surfactant monomers according to embodiments of thepresent invention would be particularly suitable in analyticalseparations of small molecules and biomolecules. Monolithic columnsaccording to embodiments of the present invention are particularlysuitable for nano-HPLC, micro-HPLC, and CEC due to the surfactantproperties of the monomer. Such monolithic materials would be suitable,for example, for use on preparative HPLC columns and solid phaseextraction disks used for isolation of positively charged drugs frombiological samples.

Monolithic columns according to the invention produced from surfactantmonomers with chain lengths of C6 or greater display enhancedelectroosmotic flow.

In particular embodiments, the surfactant-based monolithic columns havea total porosity ranging from about 60% to about 90%. In otherembodiments, the surfactant-based monolithic columns have a specificpermeability ranging from about 10⁻¹⁴ m² to about 10⁻¹² m². In yetanother embodiment, the surfactant-based monolithic columns have acumulative pore volume of about 1000 mm³/g to about 3000 mm³/g. In stillanother embodiment, the surfactant-based monolithic columns have anaverage pore diameter ranging of about 0.1 μm to about 10 μm. In anotherembodiment, the surfactant-based monolithic columns have a bulk densityranging from about 0.2 g/m³ to about 1.0 g/m³. In other embodiments, thesurfactant-based monolithic columns have a surface area greater thanabout 10 m²/g.

The present disclosure further includes a method for separating aplurality of molecules from each other comprising providing asurfactant-based monolithic column, providing a mixture of the pluralityof molecules and a mobile phase, and passing the mixture through thesurfactant-based monolithic column.

In one embodiment, the method comprises separating small polar moleculesusing embodiments of the monolithic column described herein. The presentdisclosure also includes a method for separating small nonpolarmolecules using embodiments of the monolithic column described herein.The present disclosure also includes a method of separating largebiomolecules, such as proteins, protein digests, and polypeptides, usingembodiments of the monolithic column described herein.

Embodiments of the separation methods use a mobile phase such asacetonitrile (ACN), methanol, isopropanol, tetrahydrofuran and differentkind of buffer, such as acetate buffer, ammonium acetate buffer, trisbuffer, borate buffer, or a combination thereof. In one embodiment, thesurfactant-based monolithic columns have an average resolution of about1.0 to about 2.0. In another embodiment, the surfactant-based monolithiccolumn has an analysis time of less than about 30 minutes. In stillanother embodiment, the surfactant-based monolithic column has anaverage efficiency ranging from about 10⁴-10⁶.

Without being bound by theory, it is noted that a consideration inadjusting the properties of organic polymer monoliths is the dependenceof their properties on the composition of the polymerization mixture.Such a consideration is taken into account since the column performancedepends on the morphology of the monolithic material. For polymericmonolithic columns, it is the combined pore size and the average size ofthe microglobules, which influences the performance of the column. Thus,the composition of the polymerization mixture controls the porestructure of the monolith. Therefore, varying the ratio of thecomponents of the polymerization mixture generates monolithic columnswith different properties (i.e. physical properties and chemicalproperties), from which different retention performances are produced.

Again without being bound by theory, the EOF velocity, u_(eof), may becalculated using Equation I:

$\begin{matrix}{u_{eof} = \frac{L_{eff}}{t_{0}}} & {{Equation}\mspace{14mu} I}\end{matrix}$where L_(eff) is the effective capillary length and t_(o) is themigration time of the EOF marker.

The porosity of embodiments of the monolith prepared in a capillary tubemay be measured examined by a flow method. For example, the mobile phaselinear velocity may be measured by an inert tracer (thiourea) and thevolumetric flow rate may also measured. Then, with the known empty tubedimension, the total porosity ε_(T) can be calculated using Equation II:

$\begin{matrix}{ɛ_{T} = {\frac{V}{\pi\; r^{2}c} \times 100\%}} & {{Equation}\mspace{14mu}{II}}\end{matrix}$where ε_(T) is the total porosity, V (mL/min) is the volumetric flowrate of mobile phase, r (cm) is the inner radius of the empty column, c(cm/min) is the linear velocity of mobile phase, which was determined byunretained compound thiourea. The average value of the porositiesobtained at different flow rates may be regarded as the total porosityof the monolith.

The permeability of a porous medium is a measure of its capacity totransmit a fluid driven by an imposed pressure drop. Darcy's law linkingwith the solvent viscosity and column porosity leads to the definitionof the specific permeability K⁰, which can be calculated for embodimentsof the surfactant based monolithic column using Equation III:

$\begin{matrix}{K^{0} = \frac{u\;\eta\; L\; ɛ_{T}}{\Delta\; p}} & {{Equation}\mspace{14mu}{III}}\end{matrix}$where u (m/s) is the linear velocity of eluent, η (Pa·s) is the dynamicviscosity of eluent, L is the effective column length (m), and Δp is thepressure drop (Pa).

Another aspect is further illustrated below in examples which is not tobe construed in any way as imposing limitations upon the scope of thisdisclosure. On the contrary, it is to be clearly understood that resortmay be had to various other aspects, modifications, and equivalentsthereof which, after reading the description therein, may suggestthemselves to those skilled in the art without departing from the scopeof this disclosure and the appended claims.

EXAMPLES

The following examples describe embodiments of surfactant-basedmonolithic columns prepared and used for CEC and HPLC. Thesurfactant-based monolithic columns were used to: (a) separate smallnon-polar molecules (e.g., alkyl benzenes and alkylphenyl ketones) andsmall polar molecules (e.g., polar pesticides) via CEC in Example 1, (b)separate large molecules (e.g., protein and protein digest), whichrequire gradient elution and are difficult to resolve in isocratic CECor micellar electrokinetic chromatography (MEKC), via micro-HPLC inExample 2; and (c) enhance detectability of compounds that lack a strongchromophore. CEC-MS with atmospheric pressure photoionization was usedfor separation of pesticides to provide both molecular and structuralinformation with increased selectivity and sensitivity.

Experimental design and modeling of physical and chromatographicproperties of the surfactant-based monoliths was also performed in theseexamples for the composition of the polymerization mixture. Experimentaldesign of monolithic columns is often done by varying one factor at atime while keeping the others constant (i.e. using a univariateapproach). Unfortunately, the univariate approach fails when interactionof more than one factor is involved. Hence, the univariate approach doesnot guarantee a global analysis. Multivariate design of experiment is auseful tool, which is a more efficient way to identify the experimentalfactors in monolithic column preparation.

The concentrations of the monomer, crosslinker and porogens in thepolymerization mixture, which influence the chromatographic performance(e.g., resolution, efficiency and analysis time) of the monolith, weresystematically evaluated by D-optimal experimental design. The adequacyof the polymerization model was then validated by the experimental runat the predicted conditions. The physical properties of the monolithssuch as morphology, porosity, permeability, and mechanical stabilityalso were evaluated using various analytical techniques.

Example 1 Alkylbenzene/Alkyl Phenyl Ketone Solutes for CEC and CEC-MS

Chemicals and Standards. The reagents used to produce a surfactant-basedmonolithic columns included EDMA, 1-propanol, AIBN, and11-aminoundecanoic acid, all from Aldrich (Milwaukee, Wis., USA);γ-Methacryloxypropyltrimethoxysilane, acryloyl chloride and standards ofN-methyl-carbamates (NMCs), alkylbenzenes (ABs, with side chains rangingfrom methyl to butyl group) and alkyl phenyl ketones (APKs, with sidechains ranging from methyl to octyl group) all from Sigma (St. Louis,Mo., USA). 1,4-butanediol and butyl methacrylate were purchased fromFluka (Buchs, Switzerland).

All the reagents were used as received except for the EDMA, which waspurified by distillation under vacuum prior to use using the followingprocedure: 50 mL EDMA was first filtered over a 2-cm layer of Al₂O₃using a 30 mL vacuum funnel. The filtered EDMA was then distilled undervacuum. As the distillation began, the first few drops of EDMA that camethrough the system were discarded. The distillation was allowed toproceed until only ˜5 mL, of undistilled EDMA remains in the originalround bottom flask.

Synthesis of 11-acrylamidoundecanoic acid (AAUA). The synthesis of AAUAwas a carried out as shown in Scheme 1. First, an aqueous solution ofethanol (250 ml absolute ethanol/35 ml distilled water) was used todissolve 10 g of 11-aminoundecanoic acid. To this solution, 6 g of NaOHwas added slowly until a clear solution was obtained. Next, 6 ml ofacryloyl chloride was added dropwise and the reaction mixture stirredusing a magnetic stir bar at a speed of about 7 for approximately threehours at just below 10° C., after which it was filtered. The filtratewas acidified with 1M hydrochloric acid and washed with triply deionizedwater. A white precipitate formed in the filtrate was collected byfiltration. The crude product was recrystallized from aqueous ethanol,filtered and dried by lyophilization. The purity of the AAUA was checkedby electrospray ionization mass spectrometry (ESI-MS), H¹ NMR andelemental analysis.

Preparation of Monolithic Columns.

For the preparation of stationary phases, the inner walls of capillarieswere vinylized with 3-(trimethoxylsilyppropyl methacrylate.Subsequently, AAUA, EDMA, 1-propanol, 1,4-butanediol, water, and AIBNwere mixed ultrasonically into a homogenous solution and purged withnitrogen for 10 min. A 45 cm long silanized capillary was tilled withthe polymerization mixture up to a length of 35 cm, sealed with rubberseptum, and then placed in a gas chromatography (GC) oven to polymerizefor 20 hours at 60° C. The reaction scheme for the polymerization isshown in Scheme 1. Each column of the experimental design was made induplicate. After the polymerization of the mixture, the monolithiccolumn was washed with methanol for 12 hours using a HPLC pump to removeunreacted monomers and porogens. An on-column detection window was madenext to the polymer bed using a thermal wire stripper. Finally, thecolumn was cut to 45 cm with an effective length of 30 cm.

Morphology. Pore Size and Surface Area Measurements.

The microscopic morphology of the monoliths was evaluated using scanningelectron microscope with the aid of a Hitachi X-650 (Hitachi, Japan) SEMapparatus at 7.5 kV and a filament current of 40 mA. Monolithic columnsamples were fractured, cut to a length of 2 mm, and placed on analuminum stub using a double sided carbon tape. Then, they weresputter-coated with a gold/palladium alloy using a SPI Sputter (SPISupplies Division of Structure Probe, West Chester, Pa., USA) for 1 minat 30 mA to prevent charging.

Pore-size distribution data were obtained by AutoPore IV 9500 mercuryintrusion porosimetry (MIP, Micromeritics Instrument Corporation, Ga.,USA). Surface area data were obtained by nitrogen adsorptionmeasurements performed on Micromeritics TriStar 3000 (MicromeriticsInstrument Corporation, Ga., USA). The specimens for the measurement ofpore-size distribution and surface area were prepared in parallel inglass vials under the same polymerization conditions with the samemixtures. Once the polymerization was completed, Soxhlet extraction ofthe monolith was carried out with methanol for 24 h. After drying themonoliths at 70° C. for 24 h under vacuum, nitrogen adsorption andmercury intrusion porosimetry experiments were performed.

CEC Instrumentation.

All of the electrochromatographic experiments were carried out using anAgilent CE system (Agilent Technologies, Palo Alto, Calif.) equippedwith an autosampler, a diode-array detector, 0-30-kV high-voltage powersupply and Chemstation software (V9.0) for system control and dataacquisition. A Series III HPLC pump (Lab Alliance, State College, Pa.,USA) was used for washing and equilibrating the monolithic columns withdifferent mobile phases. Fused silica capillaries (OD 375 μm, ID 100 μm)were obtained from Polymicro Technologies Inc. (Phoenix, Ariz., USA).

CEC Conditions.

The separation voltage used for CEC was +25 kV and a pressure of 12 barwas applied at both ends during the separation. The mobile phaseconsisted of 60% (v/v) ACN and 40% (v/v) 5 mmol/L phosphate buffer(pH=7.0). Before use, the mobile phase was filtered through a 0.2 μmmembrane. Samples were injected at +5 kV for 3 s, and the columntemperature was kept at 25° C. The UV detection wavelength was set to214 nm.

Calculations.

The resolution (Rs) and efficiency (N) were calculated by thechemstation software (Agilent Technologies, Palo Alto Calif.). The EOFvelocity, u_(eof), was calculated using Equation I.

The porosity of the monoliths prepared in capillaries was examined by aflow method. Briefly, the mobile phase linear velocity was measured byan inert tracer (thiourea) and the volumetric flow rate was alsomeasured. Then, with the known empty tube dimension, the total porosityδ_(T) was calculated using Equation II. The average value of theporosities obtained at different flow rates was regarded as the totalporosity of the monolith. The permeability was calculated using EquationIII.

Experimental Design.

Design-Expert (version 7.0.3, Stat-Ease, Inc. Minneapolis, Minn.) wasused to generate an experimental design, for data processing(statistical calculations), and to generate contour plots. Theexperimental design variables include five factors: A: concentration ofthe crosslinker (% EDMA), B: concentration of the monomer (% AAUA), C:concentration of 1-propanol (% 1-propanol), D: concentration of1,4-butanediol 1,4-butanediol) and E: concentration of water (% water).

The % AAUA, % EDMA, % 1-propanol, % 1,4-butanediol and % water withinthe polymerization mixture were set based on preliminary experiments.The % EDMA in the polymerization mixture was set in the range of 18.5%to 21.3%. When the % EDMA was below 18.5%, the generated monolith wasfound to have less mechanical stability. On the other hand, a % EDMAhigher than 21.3% resulted in a less effective permeability of themonolith. Having the % AAUA higher than 7.0% resulted in aninhomogeneous polymerization mixture. Therefore, 7.0% AAUA was set asthe upper limit. When the % AAUA was lower than 1.8%, the monolithiccolumn demonstrated poorer performance in CEC separation. The range ofthe % 1-propanol was 60.0% to 74.0%. For 1,4-butanediol, higher than12.0% provided an inhomogeneous monolith matrix. Hence, the %1,4-butanediol was set from 0% to 12%. As for the water content, a %water lower than 2.0%, gave lower resolution in CEC separation. However,a % water higher than 12.0%, provided an inhomogenous polymerizationmixture. The total concentration of the five components was kept at99.5% and the initiator, AIBN, Was fixed at 0.5%. These upper and lowerlimits of the factors are summarized in Table 1.

These limits generated an irregular experimental domain in whichorthogonality is not obtained. In this example, the composition of thepolymerization mixture is subjected to such restrictions, and based onthis rationale the above-described experimental design was used becauseit was appropriate for experiments where some of the factors can only bevaried over a restricted area.

The five design variables were studied at two levels, and this resultedin a final experimental matrix consisting 25 experiments. Two homologousseries of small molecular weight solutes, five ABs and seven APKs, wereused as model test analytes. The average resolution (Rs_(avg)), analysistime (R_(t), measured as the retention time of the last homologue of ABsand APKs) and average efficiency (N_(avg)) of these two series analyteswere used as the responses. All the data obtained from the actualexperiments were input into the Design-Expert software. Then, the datawere fit to a linear model, which was chosen based on the F-test andlack-of-fit test. The observed effects were tested using analysis ofvariance (ANOVA). Two-dimensional contour plots were created by thesoftware to show the interactions between factors affecting theproperties of the surfactant-based monolithic column. Finally, aparticularly desirable embodiment of a combination of all variables wasdetected using option of Derringer's desirability function available inDesign-Expert software.

Results and Discussion.

Briefly, the experimental design indicates a strong dependence ofelectrochromatogarphic parameters on the concentration of AAUA monomerand water porogen in the polymerization mixture. A difference of 6%, 8%and 13% relative standard deviation (RSD) between the predicted and theexperimental values in terms of efficiency, resolution, and retentiontime, respectively confirmed that the proposed approach was practical.Using monolithic column 3, five ABs could be completely separated around15 min and six APKs could be separated in less than 19 min. Thechromatographic results show that a particularly desirable embodiment ofthe monolithic column enabled the separation of alkyl benzenes (ABs) andalkyl phenyl ketones (APKs) homologous with efficiency up to 108,000plates/m. Thus, it was shown that this type of mixed-mode surfactant(containing both chargeable and hydrophobic sites) can be used as a CECstationary phase.

Effects of the Composition of Polymerization Mixture on theElectrohromatographic Properties.

Table 2 shows the 25-run experimental plan and the responses.

TABLE 2 Efficiency, resolution and total run time data gathered from themultivariate experimental design run order of surfactant-basedmonolithic columns. Responses Variable factors Alkylbenzenes Alkylphenylketones 1- 1,4- N_(avg) ^(c) N_(avg) ^(c) EDMA AAUA propanol butanediolwater (plates/ Rt^(b) (plates/ Rt^(b) (%) (%) (%) (%) (%) m) Rs_((avg))^(a) (min) m) Rs_((avg)) ^(a) (min) 1 21.3 7 60 0 11.2 73,000 2.2 18.872,400 3.5 22.6 2 19.9 1.8 60 5.8 12 5,000 0.7 4.8 4,500 1.0 6.4 3 18.57 60 2 12 92,100 2.4 15.4 88,900 3.3 19.8 4 21.3 7 69.2 0 2 5,400 1.06.6 5,300 1.0 9.3 5 19.9 1.8 63.8 12 2 e 0 3.4 e 0 5.1 6 21.3 4.2 60 122 5,400 0.6 8.9 5,100 1.0 6.8 7 21.3 1.8 74 0.2 2.2 e 0 1.0 e 0 0.8 818.5 1.8 67.2 0 12 6,000 0.6 6.0 5,700 0.9 5.7 9 19.2 2.9 69.6 2.05 5.7e 0 1.2 e 0 0.8 10 18.5 7 60 2 12 108,000 2.6 14.8 98,100 3.1 17.0 1119.9 1.8 63.8 12 2 e 0 1.4 e 0 0.9 12 21.3 1.8 74 0.2 2.2 e 0 1.1 e 0.10.9 13 21.3 4.2 60 12 2 3,000 0.4 3.3 2,000 0.3 4.3 14 18.5 7 72 0 27,100 0.8 5.9 6,600 0.8 6.2 15 19.9 3.6 74 0 2 e 0 1.4 e 0 1.0 16 18.5 760 12 2 3,700 0.8 3.4 3,300 1.1 4.4 17 21.3 4 62.2 0 12 25,100 1.7 9.722,700 3.0 16.4 18 19.2 2.9 64.4 3.85 9.1 4,800 0.6 3.5 4,700 0.7 4.2 1919.2 4.2 62.6 8.05 5.4 7,400 0.4 2.547 6,800 0.6 3.3 20 18.5 1.8 60 127.2 4,600 0.5 3.762 4,200 0.6 4.1 21 18.5 1.8 69.6 7.6 2 — 0 1.531 e 00.6 22 18.5 7 67 0 7 52,300 2.1 14.26 51,200 3.3 18.1 23 18.5 7 66 6 24,400 0.5 2.4 3,200 0.6 3.0 24 21.3 7 69.2 0 2 6,200 0.9 7.7 5,600 1.29.0 25 19.8 7 62.9 2.9 6.9 29,000 1.8 7.16 26,400 2.5 8.9 ^(a)Rs_((avg))is the average resolution of the five ABs or six APKs. ^(b)Rt is theretention time of the last peak of ABs or APKs. ^(c)N_(avg) is theaverage efficiency taken from the first four peaks of the ABs or APKs;e: No efficiency reported due to zero resolution.

The ranges of Rs_((avg)) were from 0 to 2.6 for ABs and 0 to 3.5 forAPKs, whereas N_(avg) ranged from 3,000 to 108,000 for ABs and 3,200 to98,100 for APKs. In addition, the Rt were as short as 1.0 min and 0.8min and as long as 18.8 min to 22.6 min, respectively, for ABs and APKs,respectively. FIG. 1 shows three of the representativeelectrochromatograms for the ABs and APKs homologous series obtainedfrom the experimental design experiments [i.e. column (i.e., run) 1,column 3 and column 7, respectively, (See Table 2)]. To summarize, theconditions were as follows: mobile phase, 60% (v/v) ACN in 5 mMphosphate buffer, pH 7.0; applied voltage +25 kV; detection, 214 nm:sample concentration, 0.8 mg/ml; electrokinetic injection, 5 kV, 3 s;for ABs (A): peak 1, thiourea; peak 2, benzene; peak 3, toluene; peak 4,ethylbenzene; peak 5, propylbenzene; peak 6, butylbenzene; APKs (B):peak 1, thiourea; peak 2, acetophenone: peak 3, propiophenone; peak 4,butyrophenone: peak 5, valerophenone; peak 6, heptanophenone; peak 7,octanophenone.

Column 7 represents one of the less desirable results among allexperiments because it showed almost no separation of homologous ABs orAPKs at all. However, column 3 and column 1 demonstrated one of the moredesirable separations for the same two classes of homologous testmixtures. This trend indicated that the composition of thepolymerization mixture has an effect on the chromatographic performanceof the yielded monolith.

A model was developed for each of the response parameters. The yieldedmodel was a mathematical equation, which was useful for identifying therelative effect of each of the factors by directly comparing the factorcoefficients. For linear regression model, the fitted equation was inthe form ofy=β ₀+β₁ A+β ₂ B+β ₃ C+β ₄ D+β ₅ E  Equation IVwhere y is the predicted response; β₀ is the intercept; β₁, β₂, β₃, β₄,β₅ are the coefficients of the five factors (A, B, C, D, and E),respectively. Positive interaction coefficients indicated thecorresponding factor was directly proportional to the response. On theother hand, the negative interaction coefficients meant the factor wasinversely proportional to the response, i.e., the bigger the factor, thesmaller the response.

The calculated empirical model was assessed by ANOVA, while the validityof the model was confirmed by checking the lack-of-fit of the model. TheANOVA data (including sum of squares, mean square, F-value, and Prob>Fvalues) for all the models are listed in Table 3. Since the ratio of themaximum response and minimum response was higher than 10 (36 for ABs and49 for APKs) for N_(avg), transformation was needed to make ANOVA thevalid. In this example, base 10 Log was recommended by the software. Foreach response (i.e., Rs_((avg)). Rt and Log₁₀N_(avg)), the sum ofsquares of the model and residual error were calculated first. Next, themean square was obtained by dividing the sum of squares with the degreeof freedom. In addition, the F-value, which was used to compare twosample variances, was calculated by dividing model mean square withresidual mean square. Prob>F is the probability value that is associatedwith the F value. In general, a term that has a Prob>F value less than0.05 would be considered a notable effect, while a Prob>F value greaterthan 0.10 was generally regarded as not significant. Furthermore, thelack-of-fit values, which are part of the residues, were also reportedto evaluate the validity of the model.

The data listed in Table 3 revealed that the models for responses(Rs_((avg)), Rt and Log₁₀N_(avg)) of ABs and APKs were all notable (witha Prob>F value less than 0.05). In addition, it was noted that theLack-of-fit values were not significant, which reveals that all themodels fit well. For example, the Rs_((avg)) of ABs showed a“Lack-of-fit F-value” of 7.15, which implied the Lack-of-fit was notsignificant relative to the pure error. There was a 6.6% chance that a“Lack-of-Fit F-value” this large could occur due to noise.Non-significant Lack-of-fit means the model gave a good fit.

TABLE 3 Analysis of Variance (ANOVA) table for the linear model of thepolymerization mixture. Sum of Mean Responses Source squares DOF squareF-value^(a) Prob > F^(b) ABs separation Rs_((avg)) Model 8.91 4 2.233.11E1 <0.0001 Residual 9.32E−1 13 7.17E−2 (error) Lack-of-fit 8.94E−110 8.94E−2 7.15 0.0660 Pure error 3.75E−2 3 1.25E−2 Corrected total 9.8417 Rt Model 4.68E2 4 1.17E2 15.70  <0.0001 Residual 1.49E2 20 7.45(error) Lack-of-fit 1.30E2 15 8.67 2.32 0.1805 Pure error 1.87E1 5 3.74Corrected total 6.16E2 24 N_(avg) Model 3.27 4 8.16E−1 1.38E1 0.0001Residual 7.69E−1 13 5.92E−2 (error) Lack-of-fit 6.94E−1 10 6.94E−2 2.780.2164 Pure error 7.49E−2 3 2.50E−2 Corrected total 4.04 17 APKsseparation Rs_((avg)) Model 1.95E1 4 4.88 2.198E1  <0.0001 Residual 2.8813 2.22E−1 (error) Lack-of-fit 2.62 10 2.62E−1 3.11 0.1898 Pure error2.53E−1 3 8.43E−2 Corrected total 2.24E1 17 Rt Model 4.15 4 1.04 2.25E1<0.0001 Residual 6.02E−1 13 4.63E−2 (error) Lack-of-fit 5.65E−1 105.65E−2 4.59 0.1176 Pure error 3.68E−2 3 1.23E−2 Corrected total 4.75 17N_(avg) Model 4.43 4 1.11 2.11E1 <0.0001 Residual 6.82E−1 13 5.25E−2(error) Lack-of-fit 5.98E−1 10 5.98E−2 2.14 0.2884 Pure error 8.38E−2 32.79E−2 Corrected total 5.11 17 ^(a)The F-Value is a term used tocompare the two variances. It is calculated from the Mean Square for theterm divided by the Mean Square of the Residual. ^(b)Probability of thenull hypothesis being true (the factor has no significant effect on theresponse) based on the F-test. In general, any term which has aprobability value less than 0.05 would be considered to have an effect.A probability value greater than 0.10 is regarded as insignificant.

To further investigate the fitness of the models, the R² (multiplecorrelation coefficient), adjusted-R², predicted-R² and adequateprecision values for the models were also evaluated and tabulated inTable 4.

TABLE 4 ANOVA table for the linear model used in the modeling of thepolymerization mixture, estimation of the validity of the fitted models.ABs separation APKs separation Rs_((avg)) Rt N_(avg) Rs_((avg)) RtN_(avg) R² 0.91 0.76 0.81 0.87 0.87 0.87 Adjusted 0.88 0.71 0.75 0.830.83 0.83 R^(2a) Predicted 0.83 0.63 0.66 0.78 0.75 0.75 R^(2b) Adequate16 13 11 14 13 13 Precision ^(a)Coefficient of determinations adjustedfor the number of terms in the model: ^(b)A measure of the amount ofvariation around the mean explained by the model, coefficient ofdetermination is based on the predicted residuals from the model.

For a good statistical model, the R² value should be close to 1.0 andthe difference between adjusted R² and predicted R² should be within0.2. For all the models, the three values were all in the acceptablerange. Table 4 also lists the “adequate precision value”. This value isan index of the signal to noise ratio and a value larger than 4 suggeststhat the model gives a good fit. The “adequate precision values” of themodels were in the range of 11 to 16, which indicated that the modelscould be used to navigate the design space.

FIGS. 2 and 3 show the regression coefficient plots for three responsesof ABs (A1-C1) and APKs (A2-C2); A 1: Average resolution (Rs_((avg)));B1: Average plates number (N_(avg)); C1: Analysis time (Rt); A2: Averageresolution (Rs_((avg))); B2: Average plates number (N_(avg)); C2:Analysis time (Rt). The 95% confidence interval was expressed in termsof error bar over the coefficient. If the coefficient was smaller thanthe interval, it indicated that the coefficient was not significantlydifferent from zero. As a result, the corresponding factor wasconsidered to be insignificant.

The regression coefficients of the Rs_((avg)) for both ABs (A1) and APKs(A2) were evaluated. At least two variables (B: % AAUA, E: % water) hadan effect on Rs_((avg)) values for both ABs and APKs. Judging from theabsolute height of the bars, it appeared that the % AAUA had the mosteffect on Rs_((avg)). This suggested that increasing the % AAUA wouldresult in more interaction sites on the stationary phase, thus providinghigher resolution for the analytes. However, the concentration ofcrosslinker EDMA had no significant effect on resolution because the 95%coefficient was smaller than the coefficient interval. Hence, there wasnot much change in the crosslinking ability of EDMA in the studiedrange. The % water had an effect that was found to be directlyproportional to the Rs_((avg)) of both classes of analytes. On the otherhand, the % l-propanol posed a indirectly proportional effect on theresolution. This trend of porogen composition indicated that at a higherconcentration of water and a lower concentration of 1-propanol, thepolarity of the polymerization solution was higher. Thus, the onset ofthe phase separation in the polymerization solution occurred earlierresulting in the formation of smaller cluster and smaller macropores.Hence, a larger surface area was obtained, resulting in higherresolution.

B1 and B2 of FIGS. 2 and 3, respectively, show the model coefficientsrelated to the response parameter Rt of ABs and APKs, respectively.Clearly, both the % AAUA and % water had directly proportional effectson the Rt. Without being bound by theory, it is believed that byincreasing the % AAUA, there will be large population of C₁₁ hydrocarbonchains on the surface of monolith. Hence, a stronger hydrophobicinteraction between the analytes and stationary phase would cause astronger chromatographic retention. As mentioned earlier, with theincrease of the % water, the polarity of the polymerization solutionwould be higher, and the macropores would be smaller. Therefore, thepresence of smaller pores would decrease the eluent flow andconsequently the speed of the analysis.

In addition to the Rs_((avg)) and Rt, Log₁₀N_(avg) of ABs and APKs wasalso reviewed. As shown, in C1 and C2 of FIGS. 2 and 3, respectively,all the five factors have directly proportional effects on theseparation efficiency. However, Log₁₀N_(avg) increased more with theincrease of the concentrations of the monomer AAUA and porogens (waterand 1,4-butanediol). However, the % water had a greater effect onLog₁₀N_(avg) than the % 1,4-butanediol. Without being bound by theory,N_(avg) depends on the retention time and peak width. An increase ofretention time and a decrease of peak width leads to an increase oftheoretical plate number. As mentioned earlier, the % AAUA and the %water have directly proportional effects on the Rt, so it was reasonablethat these two factors also an effect on the Log₁₀N_(avg). With theincrease of the % 1,4-butanediol, there is an increase in the polarityof the polymerization solution. Consequently, the polymerization mixturebecomes less soluble, which hastens the phase separation. In this way,smaller clusters are obtained. Hence the % 1,4-butanediol had a directlyproportional effect on the separation efficiency.

Contour plots, based on the calculated models, provide directinformation about the predicted responses because contour lines (alsocalled isoresponse lines) with the same predicted values of theconsidered response provide insights into the factors. As shown anddiscussed earlier, both ABs and APKs show similar trends, hence, thetwo-dimensional (2-D) plots for only ABs is shown. FIG. 4(A-C) shows the2-D contour plots for Rs_(avg)), Rt and Log₁₀N_(avg), respectively. Foreach response, the three factors having the greater effect were set onthe X1-, X2- and X3-axes and the other two factors were fixed. ForRs_((avg)), the % AAUA, % water and % 1-propanol were the three factorshaving the greater effect, so these three factors at the corners wereindicated by B, E and C as the three X-axes, while the other two factors(% EDMA and % 1-propanol) were fixed. On the other hand, for Rt andLog₁₀N_(avg), the % AAUA, % water and % 1,4-butanediol were set as thethree X-axes. Each corner of the plots corresponds to the pointsrepresenting the upper limit of each factor and the side opposite thecorner represents the lower limit of the corresponding factor. Forexample, in FIG. 4(A), the corner indicated with B stands for the upperlimit defined for the % AAUA, by moving away From this point, the % AAUAdecreases. The constraints of the factors (shown in Table 1) defined theplot region and this led to some complex regions not being covered bythe mixture design. From the 2-D contour plots, it was shown that, withthe increase of the % water, decrease of the % 1-propanol, and increaseof the % AAUA, higher resolution could be obtained. In addition, with aincrease of the % AAUA and % water, and a decrease of the %1,4-butanediol, Rt and Log₁₀N_(avg) will also increase.

Polymerization Mixture Composition for Separation of ABs and APKs withHighest Rs_((avg)) and N_(avg) Shortest Rt. From the contour plots shownin FIG. 4, it appears that the polymerization conditions required forthe highest Rs_((avg)) and N_(avg) are in conflict with the valuesneeded for the shortest Rt. One way to address this issue was to applyDerringer's desirability function D(X). This function calculates thegeometric mean of all transformed responses in the form shown inEquation V:

$\begin{matrix}{D = {\left( {d_{1} \times d_{2} \times {\ldots\ldots} \times d_{n}} \right)^{\frac{1}{n}} = \left( {\prod\limits_{i = 1}^{n}d_{i}} \right)^{\frac{1}{n}}}} & {{Equation}\mspace{14mu} V}\end{matrix}$where d_(i) is the response (in this example, Rs_((avg)) Rt and N_(avg)ABs and APKs) of interest, n is the number (in this example, six) of theresponse in the mixture design. D is the desirability that ranges from 0(the least desirable) to 1 (the most desirable). Using the Design Expertsoftware it was possible to obtain a trade-off between Rs_((avg)) orN_(avg) and Rt for ABs and APKs based on the given criteria.

The characteristics of a goal may be altered by giving a weight value ofdifferent responses. In the desirability objective function D(X), eachresponse can be assigned a weight value relative to the other responses.Weight value (r_(i)) varies from the least weighted (a value of 1), tothe higher weighted (a value of 5). If varying degrees of weight areassigned to the different responses, the objective function is shown inEquation VI:

$\begin{matrix}{D = {\left( {d_{1}^{r_{1}} \times d_{2}^{r_{2}} \times \ldots \times d_{n}^{r_{n}}} \right)^{\frac{1}{\sum r_{i}}} = {\left( {\prod\limits_{i = 1}^{n}d_{i}^{r_{i}}} \right)^{\frac{1}{\sum r_{i}}}.}}} & {{Equation}\mspace{14mu}{VI}}\end{matrix}$

If all the responses are equally weighted, the simultaneous objectivefunction reduces to the normal form of desirability.

In this example, different weight values were set for the responses. Forexample, to obtain the best compromise between analysis time vs.resolution or efficiency, a weight value of 3 was set for Rt, while forRs_((avg)) and N_(avg) weight values were 5 as seen in Table 5. Thedesired requests were fulfilled by the following solution: 18.5% EDMA,7.0% AAUA, 60.0% 1-propanol, 2.0% 1,4-butanediol and 12% water, whichcorresponded to column 3.

TABLE 5 Software values for alkylbenzene and alkyl phenyl ketoneseparation. Lower Lower Upper Goal Limit Upper Limit Weight WeightWeight EDMA is in range 18.5 21.3 1 1 3 AAUA is in range 1.8 7 1 1 31-Propanol is in range 60 74 1 1 3 1,4- is in range 0 12 1 1 3Butanediol Water is in range 2 12 1 1 3 Alkylbenzene N_(avg) maximize 14.401401 1 1 5 Rs_(avg) maximize 0 2.58 5 1 5 Rt minimize 1.073 18.816 11 1 Alkyl N_(avg) maximize 1.30103 4.380211 1 1 5 phenyl Rs_(avg)maximize 0 3.53 1 1 5 ketone Rt minimize 0.571 22.597 1 1 1

To evaluate the feasibility of this experimental design approach, thedifferences between the predicted values (which come from the model) andthe experimental values with a particularly desirable column, such ascolumn 3, were compared. The results are listed in Table 6 shows thatthe Rs_((avg)) are 2.6 and 3.3 for ABs and APKs, respectively, whichwere 8% and 3% different from the predicted values. The Rt are 15.4 minand 18.9 min, respectively, which were 16% and 13% different from thepredicted values. The efficiency values were also very close (RSD 6%) tothe predicted values. All the differences between the experimental andpredicted values were within the acceptable ranges, so this mixtureexperiment design and the modeling was proved to be valid andsuccessful.

TABLE 6 Comparison of experimental results and theoretical values forseparation of ABs and APKs on column 3. Alkylbenzene separation Alkylphenyl ketone separation Theoretical Experimental TheoreticalExperimental value value Differences value Value Differences Rs_(avg)2.2 2.4 +9% 3.3 3.3 0 Rt (min) 14.3 15.4 +8% 18.7 19.8 +6% N_(avg) 2630025200 −4% 23700 24000 +1% (plates/m)

Morphology of the Monolithic Columns. Morphology of the monolith is oneof the factors affecting the separation capability of the polymericmonolithic column. To obtain high efficiency, homogeneity and rigidityof the polymer bed is needed. SEM micrographs showed that the morphologyof the poly (AAUA-co-EDMA) monolith formed in column 1 and column 3 werevery similar, but quite different from column 7. Column 7, whichprovided very fast elution (in 1.9 min) with no resolution, had thebiggest clusters and large through-pores. On the other hand, column 1contained higher density microspheres and smaller through-pores,resulting in higher surface area. Column 3 consisted of slightly moredense morphology and tightly connected microspheres. Based on themicrographs, it appeared that the use of a higher percentage of monomerAAUA in combination with a relatively higher content of water in theporogen favored the formation of a dense monolith with smallmicrospheres. Therefore, composition of both monomer and porogensolvents seemed to have more of an effect than the % crosslinker tocontrol the morphology of the poly (AAUA-EDMA) monolith.

Porosity of the Monolithic Columns. One of the main questions incharacterizing monolithic columns is the consistency of the porositydata. To address this issue, the porosity of the monolith prepared wasexamined by mercury intrusion porosimetry (MIP), which is a dry methodthat is compared with a wet method under liquid flow conditions. First,the porosity of the monolith prepared in capillary was examined by aflow method. The mobile phase linear velocity was measured by an inertdead volume tracer (thiourea) and the volumetric flow rate was alsomeasured. Next, with the known empty tube dimensions, the total porosityε_(T) was calculated using Equation II. As shown in Table 7, the totalporosities of the examined monoliths 1, 3 and 7 were 66.5%, 74.5% and90.6%, respectively.

TABLE 7 Calculated total porosity ε_(T), permeability K, and thecalculated pore diameter d_(p). Column ε_(T) K° dp 1 66.5% 1.10599E−140.58 3 74.5% 2.87519E−14 0.88 7 90.6%  2.2258E−12 7.01

When the monolithic columns were prepared, parallel polymerization inglass vials under the same conditions with the same mixtures were alsoconducted. Nitrogen adsorption and MIP experiments were performed totest the pore-size distribution, surface area and total porosity of thebulk monolith in dry state. The trends in the ε_(T) values (shown inTable 7) tested by MIP increase in the following order: monolith1<monolith 3<monolith 7, which correlated well with the flow method.However, the ε_(T) values determined using MIP were a little lower thanthe values calculated by the flow method. These lower values obtained bythe former method could be due to the differences in the state of sample(wet vs. dry). In addition, the different polymerization containers (theflow method sample was polymerized in capillary column, while the MIPsample was polymerized in glass vials) may have also influenced theε_(T).

FIG. 5 shows pore size distributions of three of the monolithic columns:column 1, higher resolution column; column 3, column 7, lower resolutioncolumn. The pore size distributions of the three representativemonoliths show single sharp maxima in FIG. 5. Each analyte was injectedat a concentration of 0.05 mg/mL prepared in 35% ACN/H₂O. As shown, thecharacteristic pore size of monolith 1 and monolith 3 were much smaller(0.3 μm and 1-2 μm, respectively) compared to monolith 7 (10 μm). Inaddition to the pore-size distribution, several other parameters such ascumulative pore volume (V), average pore diameter (d), bulk density (ρ)and surface area (r) were also determined for the monolith andsummarized in Table 8. As expected, the poly (AAUA-co-EDMA) column 1 andcolumn 3 showed similar d and r. For example, the pore diameter of thesetwo monolithic columns were much smaller and the surface area were muchlarger compared with to the monolithic column 7, which provided thelowest CEC resolution and retention. Furthermore, the lowest V and pvalues obtained for column 1 agreed well with the lowest E_(T) valueobtained using both MIP method and the flow method.

TABLE 8 Physical characteristics of monolithic columns (1, 3 and 7):total porosity ε_(T), permeability K, cumulative pore volume V, averagepore diameter d, bulk density ρ and surface area r. determined with flowmethod determined with MIP and BET Monolithic K⁰ V d ρ r [m²/ columnε_(T) [m²] [mm³/g] [μm] ε_(T) [g/m³] g] 1 0.66 1.11E−14 1530 0.11 0.640.42 33 3 0.75 2.88E−14 1830 0.14 0.70 0.38 25 7 0.91 2.23E−12 2908 0.320.77 0.26 6.0

Permeability and Mechanical Stability.

ACN was used for the measurement of the pressure drop across the columnsat different flow rates, which could also be used to indicate themechanical stability and permeability of the columns. For the threemonolithic columns (1, 3 and 7), the specific permeability K⁰ was1.11×10⁻¹⁴ m², 2.88×10⁻¹⁴ m² and 2.23×10⁻¹² m², respectively (Table 8).The monolithic columns have a unexpectedly high permeability value,which is at least two orders greater than that of the 3 μmparticle-packed capillary column. This permeability is mainly due to thehigh total porosity of the monolith allowing liquids to flow through thecolumn under low pressure. Plots of the volumetric flow rate of ACNagainst the applied pressure for monolithic column 1, 3 and 7 are shownin FIG. 6. For each measured column, the back pressure's dependencyagainst flow rate of the solvent is a straight line with the correlationcoefficient R better than 0.999. This indicated that permeability andmechanical stability of the monolith are both good.

Effect of Acetonitrile on Electrochromatographic Retention andEfficiency of the Monolithic Columns.

The electrochromatographic retention and efficiency of the column 3 weretested using homologous ABs and APKs. Effects of concentration of ACN onthe chromatographic retention capacities of ABs and APKs homologous werestudied in the range of 50-80% (v/v). The linear dependence plots of thelog k′ of ABs and APKs versus concentration (v/v) of ACN in the mobilephase are shown in FIG. 7. The good linearity confirmed that theAAUA-EDMA monolithic column 3 provided a reverse-phase separationmechanism over a wide range of ACN composition. As expected, atequivalent concentration of acetonitrile the more polar APKs homologuesare retained less than the corresponding ABs. Nevertheless, for bothhomologues series, an acetonitrile composition of 70% (v/v) in themobile phase was found to provide the best compromise between resolutionand efficiency versus analysis time.

The peak efficiency of the three monolithic columns was also evaluated.To investigate the separation performance under different voltage, theplate height was measured as a function of mobile phase linear velocityby varying the applied voltage from 2 to 30 kV. The Van Deemter plotsfor the investigated columns in FIG. 8 demonstrate the dependence of theaverage plate height of homologous ABs and APKs and thiourea on the EOFand applied voltage on column 3. The plate height is the average takenfor the AB and APK homologues series. For thiourea, with the increase ofapplied voltage, the linear flow rate increased and the plate heightdecrease sharply at first. However, at voltage higher than 15 kV, theplate height almost kept constant. As expected, for ABs and APKs, theirefficiencies were a little lower than thiourea at the same voltage. Thehyperbolic shape of the Van Deemter curves and lowest H obtained for ABsand APKs at high flow velocity similar to those reported in literaturewith other types of monolithic phases. On average, the plate heightswere approximately 39 μm and 27 μm for ABs and APKs respectively in thevelocity range of the experiment.

Reproducibility.

The reproducibility of column fabrication was assessed as (a)intra-batch (column to column) and (b) inter-batch (batch-to-batch).Three separate batches of monolithic column were prepared and for eachbatch, three columns were made for a total of 9 columns. Apolymerization mixture was prepared for each of the three batches. Theretention times of ABs and APKs were selected to evaluate thereproducibility of the fabrication process. From the data shown in Table9, it can be seen that the RSD values of the retention time are lowerthan 3%. The intra-batch precision of retention time ranged from 0.98 to2.14, whereas the inter-batch precision of retention time (calculated asthe average of 3 batches) ranged from 0.79 to 2.75. These data suggestthat the preparation of the monolith was reproducible.

TABLE 9 Intra-batch and Inter-batch reproducibility of retention timefor alkylbenzenes and alkyl phenyl ketones in CEC using monolithiccolumn 3. Rt (avg), min (% RSD) B C A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 B6 1 28.42 9.00 10.24 12.31 14.61 6.86 7.90 9.21 10.79 15.99 19.92 (2.14)(1.53) (1.69) (1.23) (1.96) (0.72) (1.35) (0.95) (1.11) (0.84) (1.26) 23 8.53 9.12 10.17 12.42 14.84 6.80 7.81 9.30 10.91 15.85 19.70 (2.05)(1.87) (1.05) (0.98) (1.27) (0.62) (1.24) (1.14) (1.85) (1.01) (1.51) 33 8.37 8.90 10.09 12.16 14.78 6.92 8.07 9.13 10.80 16.12 20.19 (1.98)(2.11) (1.24) (1.25) (1.83) (0.73) (1.04) (1.24) (2.01) (1.54) (1.19) O8 8.44 9.01 10.17 12.30 14.74 6.86 7.83 9.21 10.93 15.98 19.94 (2.75)(2.92) (1.86) (1.44) (2.65) (0.79) (1.47) (1.59) (2.36) (2.27) (2.31) Rt(avg): average retention time. A1-A5: benzene, toluene, ethylbenzene,propylbenzene, butylbenzene; B1-B6: acetophenone, propiophenone,butyrophenone, valerophenone, heptanophenone, octanophenone. B: batch C:column O: overall

FIG. 9 shows CEC-MS of N-methylcarbamates (NMCs) pesticides obtained onthe monolithic column 3. Conditions: monolithic column, 60 cm totallength (40 cm effective length)×100 μm ID; mobile phase, 5 mM ammoniumacetate, pH 6.5, at 35% (v/v) ACN; applied voltage, +30 kV; 12 bar inletpressure; electrokinetic injection, +10 kV for 5 s. APPI parameters: SIMmode; fragment voltage, 60 v; nebulizer pressure, 5 psi: drying gas flowrate, 2 L/min; drying gas temperature, 100° C.; vaporizer temperature250° C.; capillary voltage, 2500 v. Sheath liquid, 5 mM ammoniumacetate, 2% (v/v) acetoneinin 50/50 (v/v) MeOH/H₂O; sheath liquid flowrate 20 μL/min. Analytes: 1, oxamy; 2, methomyl; 3, aldicarb; 4,primicarb; 5, propoxur; 6, bendiocarb; 7, isoprocarb; 8, carbaryl; 9,methiocarb.

Conclusions.

A surfactant-based poly(AAUA-co-EDMA) monolith was prepared as one-steppolymerization (after the synthesis of AAUA monomer). The evaluation ofthe polymerization mixture (concentration of crosslinker, monomer andprogens) was achieved using experimental design of the mixture. Theconcentration of monomer (AAUA) and water are the two factors studiedwhich affect the monolith formation the most. The polymerizationconditions predicted from the desirability function was tested. Theexperimental data had in very good to excellent agreement with thepredicted results. The results showed that the experimental designmethod is a very promising approach to obtain desirable polymerizationconditions, allowing the successful development of a monolithicstationary phase. In addition, the column presented typicalpolymer-based monolith morphology, excellent permeability and goodmechanical stability. Furthermore, the inter- and intra-batchreproducibility of column fabrication was good for practicalapplications.

Example 2 Protein Solutes for HPLC

Chemicals and Standards.

The materials and methods for forming embodiments of surfactant-basedmonolithic columns used in Example 1 were also used in Example 2. Inaddition, ribonuclease A, cytochrome c and myoglobin were purchased fromSigma (St. Louis, Mo., USA) and were used as received.

Capillary HPLC Instrumentation.

The HPLC chromatographic experiments were carried out on an Ultra-Plus &Ultra-Plus II Micro LC system (Micro-Tech Scientific, Sunnyvale, Calif.,USA) equipped with a Data Module UV-visible detector (wavelengthcontinuously adjustable) and Chrom Perfect® (Version 5.1, JusticeLaboratory Software, New Jersey) software. A Series III HPLC pump (LabAlliance, State College, Pa., USA) was used for washing andequilibrating the monolithic column.

HPLC Chromatographic Conditions.

Gradient elution was used for the protein separation in capillary HPLC.Mobile phase A comprised 98% ACN with 0.1% TFA; and mobile phase Bcomprised 2% ACN with 0.1% TFA. A linear gradient program, 16% A at 0min, 40% A at 0.5 min. Ultraviolet (UV) detection was carried out at 214nm.

Tryptic Protein Digest.

Myoglobin was dissolved in 50 mM ammonium bicarbonate to a concentrationof 1 mg/mL. Tryptin was added at a substrate-to-enzyme ratio of 100:1,and then the solution was incubated overnight at 37° C. Then, the digestwas vacuum-dried and reconstituted in water without and additionalcleanup steps before analysis.

Calculations.

The resolution (Rs) and efficiency (N) were calculated by the ChromPerfect® software.

Experimental Design.

Design-Expert (version 7.0.3, Stat-Ease, Inc. Minneapolis, Minn.) wasused to generate D-optimal experimental designs, data processing(statistical calculations), and contour plots. The experimental designvariables include the same five factors, with the same upper and lowerlimits, as the experimental design of Example 1. Three proteinsribonuclease A, cytochrome c and myoglobin were used as model testanalytes. Average resolution (Rs_((avg))), analysis time (R_(t),measured as the retention time of the last protein myoglobin) andaverage efficiency (N_(avg)) were used as the responses. All the dataobtained from the actual experiments were input into the Design-Expertsoftware. The data were fitted into linear model which was chosen basedon the F-test and lack-of-fit test. The observed effects were tested forsignificance using ANOVA. The 2-D contour plots were created by thesoftware to show the interactions between factors. Finally, aparticularly desirable embodiment of a combination of all variables wasdetected using a desirability function available in Design-Expertsoftware.

Results and Discussion.

Table 10 demonstrates the 25-run experimental plan and the responses.

TABLE 10 Efficiency, resolution and total run time data gathered fromthe multivariate experimental design run order for surfactant-basedmonolithic columns. Variable factors Responses EDMA AAUA 1-propanol1,4-butanediol water Rt^(b) N_(avg) ^(c) Col. (%) (%) (%) (%) (%) (min)Rs_((avg)) ^(a) (plates/m) 1 21.3 7 60 0 11.2 n.a. n.a. n.a. 2 19.9 1.860 5.8 12 3.8 2.8 33200 3 18.5 7 60 2 12 36 12.8 502000 4 21.3 7 69.2 02 3.3 5.9 75000 5 19.9 1.8 63.8 12 2 7.5 5.4 158000 6 21.3 4.2 60 12 26.0 5.7 167000 7 21.3 1.8 74 0.2 2.2 1.9 1.3 3100 8 18.5 1.8 67.2 0 123.9 4.0 75700 9 19.2 2.9 69.6 2.1 5.7 2.0 2.1 8700 10 18.5 7 60 2 12 3012.4 485000 11 19.9 1.8 63.8 12 2 2.5 5.0 49300 12 21.3 1.8 74 0.2 2.22.1 1.2 4700 13 21.3 4.2 60 12 2 2.7 4.7 50300 14 18.5 7 72 0 2 2.1 2.913200 15 19.9 3.6 74 0 2 2.5 2.8 15100 16 18.5 7 60 12 2 5.8 5.1 10400017 21.3 4 62.2 0 12 15 8.4 334000 18 19.2 2.9 64.4 3.9 9.1 2.8 3.7 5090019 19.2 4.2 62.6 8.1 5.4 2.2 3.8 34400 20 18.5 1.8 60 12 7.2 2.8 2.527800 21 18.5 1.8 69.6 7.6 2 2.0 0.9 1600 22 18.5 7 67 0 7 10 7.1 25000023 18.5 7 66 6 2 2.1 3.7 25800 24 21.3 7 69.2 0 2 2.6 2.8 26200 25 19.87 62.9 2.9 6.9 5.7 6.3 216000 ^(a)The analysis time is the retentiontime of the last peak (myoglobin); ^(b)Average resolution of the threeproteins (ribonuclease A. cytochrome c and myoglobin); ^(c)Averageplates number of the three proteins; n.a.: Not available.

The ranges of Rs_((avg)) were found to be from 0.9 to 12.8, whereasN_(avg) ranged from 1600 to 502,000. In additionally, the Rt were asshort as 1.9 min and as long as 36.0 min. FIG. 10 shows two of therepresentative chromatograms for the proteins obtained from theexperimental design experiments (i.e. column 3 and column 7),respectively. Conditions: mobile phase A, 0.01% TFA in ACN, mobile phaseB, 2% ACN, 0.01% TFA in water; linear gradient program, 16% A at 0 min,40% A at 0.5 min; injection size, 0.6 s; total flow rate, 100 μL/min;detection, 214 nm. Peak 1, ribonuclease A; peak 2, cytochrome c; peak 3,myoglobin. Each analytes was injected at concentration of 0.3 mg/mL inwater. Column 7 (a) represented one of the fastest separations among allexperiments. However, column 3 (b) demonstrated one of the separationswith highest resolution for the three proteins. This trend indicatedthat the composition of the polymerization mixture affected thechromatographic performance of the yielded monolith.

A mixture quadratic model was developed for each of the responseparameters. The yielded model was a mathematical equation which wasuseful for identifying the relative effect of the factors by directlycomparing the factor coefficients. For mixture quadratic model, thefitted equation is in the form ofy=β ₀+β₁ A+β ₂ B+β ₃ C+β ₄ D+β ₅ E+β ₁₂ AB+β ₁₃ AC+β ₁₄ AD+β ₁₃ AE+β ₂₃BC+β ₂₄ BD+β ₂₅ BE+β ₃₄ CD+β ₃₅ CE+β ₄₅ DE  Equation VIIwhere, y is the predicted response. β₀ is the intercept. The first-ordermixture-model coefficient β_(n) (n=1, 2, 3, 4, 5) is the coefficient forthe input factor (A, B, C, D and E) which predicts the response from thepure components. β₁₂, β₁₃, β₁₄ . . . is the coefficient for the twofactors interaction (AB, AC, AD . . . ), which describes the effect oftheir interaction on the response. Positive interaction coefficientsindicate the corresponding factor is directly proportional to theresponse. On the other hand, the negative interaction coefficients meansthe factor is inversely proportional to the response, i.e., the biggerthe factor, the smaller the response. It should be mentioned that, forN_(avg), because the ratio of the maximum response and minimum response,314, was much higher than 10, transformation was needed to make theANOVA valid. In this example, base 10 Log was recommended by thesoftware. In other words, models for Log₁₀N_(avg) were obtained.

The calculated empirical model was assessed by ANOVA, while the validityof the model was confirmed with checking the lack-of-fit of the model.The ANOVA data (including sum of squares, mean square, F-value andProb>F values, R², Adj-R², Pred-R², Adeq-R²) for all the models arelisted in Table 11. For each response (i.e. Rs_((avg)), Rt andLog₁₀N_(avg)), the sum of squares of the model and residue error werecalculated first. Next, the mean square was obtained by dividing the sumof squares with the degree of freedom. In addition, the F-value, whichwas used to compare two sample variances, was calculated by dividingmodel mean square with residual mean square. Prob>F is the probabilityvalue that is associated with the F value. In general, a term that has aProb>F value less than 0.05 would be considered a notable effect, whilea Prob>F value greater than 0.10 is generally regarded as notsignificant. Furthermore, the lack-of-fit values, which are part of theresidues, are also reported to evaluate the validity of the model.

TABLE 11 Sum of Mean Adj- Pred- Adeq- Source squares DOF squareF-value^(a) Prob > F^(b) R² R² R² R² Rs_((avg)) Model 2.13E2 14 1.52E12.38E1 <0.0001 Residual 5.75 9 6.39E−1 (error) Lack-of-fit 0.23 45.75E−2 5.23E−2 0.9930 Pure error 5.52 5 1.10 Corrected 2.19E2 23 0.970.93 0.85 18 total Rt Model 1.72E3 14 1.22E2 2.06E1 <0.0001 Residual5.34E1 9 5.93 (error) Lack-of-fit 1.84E1 4 4.60 6.56E−1 0.6483 Pureerror 35.04 5 7.01 Corrected 1.77E3 23 0.97 0.92 0.75 18 total N_(avg)Model 9.87 14 7.05E−1 1.15E1 0.0004 Residual 5.50E−1 9 6.11E−2 (error)Lack-of-fit 1.70E−1 4 4.25E−2 5.59E−1 0.7132 Pure error 3.80E−1 57.60E−2 Corrected 1.04E1 23 0.95 0.86 0.71 13 total ^(a)The F Value fora term is the test for comparing the variance associated with that termwith the residual variance. It is the Mean Square for the term dividedby the Mean Square for the Residual. ^(b)This is the probability valuethat is associated with the F Value for this term. It is the probabilityof getting an F Value of this size if the term did not have an effect onthe response. In general, a term that has a probability value less than0.05 would be considered a notable effect. A probability value greaterthan 0.10 is generally regarded as not significant.

The data listed in Table 11 revealed that the models for responses(Rs_((avg)), Rt and Log₁₀N_(avg)) of the proteins with a Prob>F valueless than 0.05. In addition, note that the lack-of-fit values are notsignificant (with a Prob>F value greater than 0.1) which reveals thatall the models fit well. Take Rs_((avg)) for example, the “Lack-of-fitF-value” of 5.75E-2 implied the Lack-of-fit is not significant relativeto the pure error. There was a 5.23% chance that a “Lack of Fit F-value”this large could occur due to noise. Non-significant lack of fit meantthe model gave a good fit.

In order to further investigate the fitness of the models, the R²(multiple correlation coefficient), adj-R², pred-R² and adequateprecision values (Adeq-R²) for the models were evaluated (Table 11). Fora good statistical model, R² value should be close to 1.0 and differencebetween adj-R² and pred-R² should be within 0.2. For all the models, thethree values were all in the acceptable range. Table 11 also lists theAdeq-R². This value is an index of the signal to noise ratio and a valuebigger than 4 suggests that the model gives a good fit. The adeq-R² ofthe models was 18, 18 and 13, respectively, and this indicated that themodels can be used to navigate the design space.

FIGS. 11A-C shows the regression coefficient plots for the threeresponses (Rs_((avg)), Rt and Log₁₀N_(avg), in that order). The 95%confidence interval is expressed in terms of error bar over thecoefficient. If the coefficient was smaller than the interval, itindicated that the coefficient is not significantly different from zero.As a result the corresponding factor was considered to be insignificant.The coefficients of the second-order terms will not be discussed in thefollowing sections because of their lack of chemical denotations

From the regression coefficient plots, it was seen that factors D: %1,4-butanediol and E: % water had directly proportional effects on theresponses Rs_((avg)), Rt and N_(avg), which maybe attributed to the factthat the increase of the % 1,4-butanediol and % water hastened the onsetof the phase separation during the polymerization process resulting inthe formation of smaller cluster and smaller macropores. Hence, a largersurface area was obtained resulting in higher resolution. In addition,according to the theory that the retention time is largely dependent onthe size of the macropores, a higher % 1,4-butanediol and higher % waterwill make a monolithic column with smaller macropore size, whichinfluences the speed of the eluent flow and therefore the speed of theanalysis. Furthermore, as expected, with smaller cluster, larger surfacearea and smaller macropores, higher separation efficiency would beobtained.

A close examination of FIGS. 11A-C revealed that besides the first orderterms, two cross terms (CE and DE) had a notable effect on Rs_((avg))and Rt, four cross terms (AC, AD, AE and DE) had a notable effect on toN_(avg). The effect of these cross terms indicates that although thesingle term is not significant, when they combine with other terms, theyhad a notable effect. For example, factor C, % 1-propanol, is notsignificant to Rs_((avg)) or Rt, however, it has an effect as acooperative term when combined with term E, % water. Similarly, term A,% EDMA, is not significant to N_(avg) as a single factor, but whencombined with factor C. D or E, has an effect.

FIGS. 12A-C show the 2-D contours plots for Rs_((avg)), Rt andLog₁₀N_(avg), respectively. For each response, the three factors whichhad more of an effect on the response were set as the X1-, X2- andX3-axes and the other two factors were fixed. In this example, the %AAUA, % 1,4-butanediol and % water had more of an effect on Rs_((avg))and Rt, so these three factors at the corners indicated by B, E and Care set as the three X-axes, while the other two factors (% EDMA and %1-propanol) were fixed. However, for Log₁₀N_(avg), % AAUA, %1,4-butanediol and % water were set as the X1-, X2- and X3-axes. Eachcorner of the plots corresponds to the points representing the upperlimit of each factor and the side opposite the corner represents thelower limit of the corresponding factor. For example, in FIG. 12A, thecorner indicated with B stands for the upper limit defined for the %AAUA, by moving away from this point, % AAUA decrease. The constraintsof the factors (shown in Table 1) defined the plot region and this ledto some complex regions cannot be covered by the mixture design. Fromthe 2-D contour plots (shown in FIG. 12A-C), it can be seen that, withthe increase of the % water, decrease of % l-propanol, and increase ofthe % AAUA, higher resolution and longer retention time could beobtained. In addition, with a increase of the % water, and a decrease ofthe % 1,4-butanediol, Log₁₀N_(avg) will increase.

Polymerization Mixture Composition for Separation of Proteins.

From the contour plots shown in FIGS. 12A-C, it appears that thepolymerization conditions required to improve Rs_((avg)) and N_(avg) arein conflict with the values needed to improve the Rt for fast proteinseparation and high resolution separation. One way to address thisproblem is to apply Derringer's desirability function D(X).

In this example, different weight values were set for the responses. Forfast separation solution, to obtain the best compromise between analysistime vs. resolution, a weight value of 5 was set for the minimization ofRt, while for Rs_((avg)), weight values were 1, as shown in Table 12.

TABLE 12 Software values of fast separation and high resolutionseparation of proteins. Lower Upper Goal Lower Limit Upper Limit WeightWeight Weight EDMA is in 18.5 21.3 1 1 3 range AAUA is in 1.8 7 1 1 3range 1-Propanol is in 60 74 1 1 3 range 1,4-Butanediol is in 0 12 1 1 3range Water is in 2 12 1 1 3 range For fast Rt minimize 1.9 36.1 1 1 5separation Rs_((avg)) maximize 0.9 12.8 1 1 1 For high N_(avg) maximize1600 501700 1 1 3 resolution Rs_((avg)) maximize 0.9 12.8 1 1 5separation Rt: The analysis time is the retention time of the last peak(myoglobin); Rs_((avg)): Average resolution of the three proteins(ribonuclease A, cytochrome c and myoglobin); N_(avg): Average platesnumber of the three proteins.

The desired requests were fulfilled by the following solution: 20.3%EDMA, 7.0% AAUA, 68.3% 1-propanol, 0% 1,4-butanediol and 3.9% water. Forhigh resolution separation solution, to obtain a compromise betweenefficiency vs.

resolution, a weight value of 3 was set for the maximization of N_(avg),while for Rs_((avg)), weight values were 5. The desired requests werefulfilled by the following solution: 18.5% EDMA, 7.0% AAUA, 60.0%1-propanol, 2.0% 1,4-butanediol and 12% water.

Chromatograms of the protein separation using the solution monolithiccolumns are shown in FIG. 13. Judging from the chromatograms, threeproteins could be separated in 2.5 min with an average resolution 5.0 onthe fast separation column (OF-1), while, the same analytes could beseparated in 32 min with a resolution as high as 12.8 and an efficiencyas high as 502,000 for the high resolution column (OH-1).

In order to evaluate the feasibility of this experimental designapproach, the differences between the predicted values (which come fromthe model) and the experimental values with the solution columns werecompared. The results are listed as an inset table in FIG. 13. For thefast separation column, it was found that, the Rs_((avg)) and Rt are 5.0and 2.5 min, respectively, which are 5.7% and 4.2% different from thepredicted values. For the high resolution separation column, theRs_((avg)) and N_(avg) are 12.8 and 502,000, respectively, which are1.6% and 0.2% different from the predicted values. The efficiency valueswere also close to the predicted values. All the differences between theexperimental and predicted values were within the acceptable ranges, sothis mixture experiment design and the modeling was proved to be validand successful.

In addition, a tryptic digest of myoglobin was used to further evaluatethe performance of the high resolution column in μ-HPLC. Compared withthe fast separation column OF-1 (FIG. 14( a)), the high resolutioncolumn OH-1 (FIG. 14( b)), could successfully separate 13 peaks of thetryptic digest of myoglobin. Conditions: mobile phase A, 0.01% TFA inACN, mobile phase B, 2% ACN, 0.01% TFA in water; linear gradientprogram, 16% A at 0 min, 20% A at 10 min, 50% A at 15 min, 80% A at 20min; injection size. 0.6 s; total flow rate. 100 μL/min; detection, 214nm. Sample, 1.0 mg/mL myoglobin trypsin digest in water.

Morphology of the Monolithic Columns.

The morphology of the poly (AAUA-co-EDMA) monolith formed in column 7and OF-1 are very similar, but quite different from column 10. Column 7,which provided very fast elution (in 1.9 min), had the biggest clustersand the largest through-pores. The fast separation monolith (columnOF-1) consisted of slightly more dense morphology and tightly connectedmicrospheres. On the other hand, column 10, the high resolution column,contained higher density microspheres and smaller through-poresresulting in higher surface area. Compared the two monoliths, OH-1consisted of smaller clusters and beads, while column OF-1 containedlower density clusters and bigger through-pores which made the highpermeability and convection mass transfer possible.

Porosity of the Monolithic Columns.

The consistency of the porosity data was evaluated using the methodsdescribed in Example 1. As shown in Table 13, the total porosities ofthe examined monoliths 7, 10 (OH-1) and OF-1 were 86%, 72% and 79%,respectively.

TABLE 13 Pore characteristics of monolithic columns (#7, #10 and OF-1):total porosity ε_(T), permeability K, cumulative pore volume V, averagepore diameter d, bulk density ρ and surface area r. determined with flowmethod determined with MIP and BET K V d ρ r Column ε_(T) (m²) [mm³/g][μm] ε_(T) [g/m³] [m²/g] 7 0.86 2.23E−12 2908 37 0.32 0.26 6 10/OH-10.72 4.60E−14 1830 51 0.14 0.38 25 OF-1 0.79 1.33E−12 2840 38 0.30 0.2610

The trends in the ε_(T) values (shown in Table 13) tested by MIPincrease in the following order: monolith 10(OH-1)<monolithOF-1<monolith 7, which correlated well with the flow method. However,the ε_(T) values determined using MIP were a little lower than thevalues calculated by the flow method. These lower values obtained by theformer method could be due to the differences in the state of sample(wet vs. dry). In addition, the polymerization container (the flowmethod sample was polymerized in capillary column while the MIP samplewas polymerized in glass vials) may have also influenced the ε_(T).

The pore size distributions of the three representative monoliths showsharp maxima in FIG. 15. As shown, the characteristic pore size ofmonolith 10 was smaller in size (1˜2 μm) compared to monolith 7 (˜10 μm)and column OF-1 (˜8 μm). In addition to the pore-size distribution,several other parameters such as cumulative pore volume (V), averagepore diameter (d), bulk density (ρ) and surface area (r) were alsodetermined for the monolith and are summarized in Table 13. As expected,the poly (AAUA-co-EDMA) column 7 and column OF-1 showed similar d and r.For example, the pore diameters of these two monolithic columns weremuch larger and the surface areas were much smaller compared to themonolithic column 10, which provided the highest protein resolution andretention. Furthermore, the lowest V and ρ values obtained for column 10agreed % veil with the lowest e_(r) value obtained using both MIP methodand the flow method.

Permeability and Mechanical Stability.

ACN was used for the measurement of the pressure drop across the columnsat different flow rates, which could also be used to indicate themechanical stability and permeability of the columns. For the threemonolithic columns (7, 10(OH-1) and OF-1), the specific permeability K⁰was 2.23×10⁻¹² m², 4.60×10⁻¹⁴ m², 1.33×10⁻¹² m² and, respectively. Themonolithic columns had high permeability values, which was at least twoorders greater than that of a 3 μm particle-packed capillary column.This high permeability was mainly due to the high total porosity of themonolith, allowing liquids to flow through the column under lowpressure. Plots of the volumetric flow rate of 100% ACN against theapplied pressure for monolithic column 7, OH-1 and OF-1 are shown inFIG. 16. Thiourea was used as dead time marker. For each measuredcolumn, the back pressure's dependency against flow rate of the solventwas a straight line with the correlation coefficient R better than0.999. This correlation coefficient indicated that permeability andmechanical stability of the monolith were both good.

Chromatographic Properties of the Columns.

The peak efficiency of the three monolithic columns also was evaluated.To investigate the separation performance under a different voltage, theplate height was measured as a function of mobile phase linear velocity.Van Deemter plots showing average plate height of proteins as a functionof mobile-phase flow velocity are shown in FIG. 17. Column OH-1 gavehigh separation efficiency, and can have a plate height as low as 0.7 μmat a flow velocity of 0.3 mm/sec in a range of 0.5 to 4.0 mm/sec, with alittle fluctuation for the plate height. For column OF-1, the lowestplate height was around 4 μm at a flow rate of 8 mm/sec. Thus, themonolithic columns could achieve a fast separation without sacrificing alot of separation efficiency, especially when compared with packedcapillary column.

Stability and Reproducibility.

To evaluate the chromatographic stability, monolithic columns made withthe OF-1 and OH-1 polymerization mixtures were utilized to conductcontinuous 5 injections on a daily basis for three consecutive days(i.e., a total of 15 injections were performed on each column). For thecolumns OF-1 and OH-1, the RSD values of the retention times and numberof plates are shown in Table 14. For column OF-1, it was found that theinter-day precision of retention time ranged between 0.20% and 0.53%,and the RSD for the number of plates were in the range of 4.15% to7.24%; the intra-day precision of retention time as the mean of 3 daysranged between 0.38% and 0.75%, and the RSD for the number of plateswere in the range of 6.31% to 8.59%. For column OH-1, it was found thatthe inter-day precision of retention time ranged between 0.44% and0.76%, and the RSD for the number of plates were in the range of 4.23%to 8.26%; the intra-day precision of retention time as the mean of 3days ranged between 0.56% and 0.87%, and the RSD for the number ofplates were in the range of 6.57% to 9.00%. Thus, the chromatographicperformance stability of the monoliths was acceptable.

TABLE 14 Intra day and Inter day reproducibility of retention time andseparation efficiency for proteins in μ-HPLC using column OF-1 and OH-1for consecutive 3 days. Day Rt (avg), min (% RSD) N_(avg), plates/m (%RSD) no. run Ri A Cyo C Myo Ri A Cyo C Myo Column OF-1 1 5 2.03 2.352.62 42900 73000 37900 (0.43) (0.55) (0.20) (4.95) (6.21) (5.87) 2 52.02 2.34 2.63 49500 68400 42100 (0.41) (0.56) (0.21) (4.15) (7.24)(4.42) 3 5 2.03 2.36 2.63 45800 72100 39500 (0.42) (0.53) (0.22) (5.21)(6.51) (5.23) Overall 15 2.03 2.35 2.63 46100 71200 39800 (0.75) (0.59)(0.38) (6.31) (8.59) (6.91) Column OH-1 1 5 24.07 26.69 31.02 612000672000 268000 (0.63) (0.72) (0.42) (6.02) (4.23) (7.32) 2 5 24.15 26.6531.13 651000 721000 310000 (0.71) (0.62) (0.45) (6.45) (5.21) (7.31) 3 524.01 26.52 31.05 601000 623000 234000 (0.79) (0.57) (0.39) (5.56)(5.35) (8.26) Overall 15 24.08 26.62 31.07 621000 672000 271000 (0.84)(0.87) (0.56) (7.79) (6.57) (9.00) Rt (avg): average retention time;N_(avg): average plates number.

To study the batch-to-batch column reproducibility, three batches ofcolumns were prepared and for each batch, three columns were made usingthe same polymerization mixtures. Thus, 9 columns were made in threebatches to study the preparation reproducibility. From the results shownin Table 15, it was found that for column OF-1 all the RSD values of theretention time were lower than 1.76%, and for column OH-1 all the RSDvalues of the retention time were lower than 2.04%, these proved thatthe preparation of the monolith was reproducible.

TABLE 15 Intra batch and Inter batch reproducibility of retention timeand separation efficiency for proteins separation in μ-HPLC using columnOF-1 and OH-1. Batch Rt (avg), min (% RSD) N_(avg), plates/m (% RSD) No.Col. Ri A Cyo C Myo Ri A Cyo C Myo Column OF-1 1 3 2.03 2.31 2.63 4810069200 65200 (1.56) (1.01) (0.96) (9.57) (10.20) (8.65) 2 3 2.02 2.342.62 46200 65100 63200 (0.56) (1.01) (1.05) (8.35) (11.34) (6.31) 3 32.03 2.29 2.58 50300 59800 57900 (1.23) (0.95) (1.02) (9.24) (12.24)(7.25) Overall 9 2.03 2.31 2.61 48200 64700 62100 (1.76) (1.09) (1.15)(10.51) (13.54) (9.21) Column OH-1 1 3 24.12 26.86 31.25 624000 687000294000 (1.25) (1.41) (1.22) (7.21) (8.54) (9.35) 2 3 24.07 26.34 31.17601000 710000 315000 (1.67) (1.72) (1.05) (8.56) (9.41) (8.54) 3 3 24.2126.57 31.05 657000 694000 284000 (1.52) (1.36) (1.31) (8.47) (10.25)(10.27) Overall 9 24.13 26.59 31.13 627000 697000 294000 (2.04) (1.85)(1.53) (9.31) (11.13) (11.35) Rt (avg): average retention time; N_(avg):average plates number.

Conclusions.

The evaluation of the polymerization mixture (concentration ofcrosslinker, monomer and porogens) was achieved using experimentaldesign of the mixture. The concentration of 1,4-butanediol and water arethe two factors studied which affect the monolith formation the most.Polymerization mixtures for fast separation column and high resolutioncolumn were processed from the experimental design. These polymerizationconditions predicted from the desirability function were tested. Theexperimental data was in good agreement with the predicted results.Differences less than 6% between the predicted and the experimentalvalues in terms of efficiency, resolution, and retention time indeedconfirmed that the proposed approach is practical. Using the OF-1 andOH-1 columns, a completed fast separation of proteins could be obtainedin 2.5 min and tryptic digest of myoglobin separation was successfullyconducted on the high resolution column. These columns were alsovalidated using proteins and protein digest. The results showed that theexperimental design method is a very promising approach to obtaindesirable polymerization conditions, allowing the successful developmentof a monolithic stationary phase. The columns presented polymer-basedmonolith morphology, excellent permeability, and good mechanicalstability. Furthermore, the monolithic columns demonstrated good inter-and intra-day repeatability as well as excellent the inter- andintra-batch reproducibility of column fabrication.

It should be understood that the foregoing relates to particular aspectsand that numerous changes may be made therein without departing from thescope of this disclosure as defined from the following claims.

We claim:
 1. A process for preparing a surfactant monomer, the processcomprising: providing a carboxylic acid having a carbon chain lengthranging from about 6 to about 20 and a tail group, wherein the tailgroup comprises NH₂, or OH; reacting the carboxylic acid with aryloylchloride to form a first product; reacting the first product with1-hydroxypyrrolidine-2,5-dione to form a second product; and reactingthe second product with an amino acid to form the surfactant monomerincluding an amino acid functional group.
 2. The process of claim 1,wherein the amino acid valine, nor-valine, leucine, isoleucine,tert-leucine, nor-leucine, aspartic acid, glutamic acid, arginine,histidine, tryptophan, tyrosine, cysteine, threonine, serine, proline,or glycine.
 3. The process of claim 1, wherein the surfactant monomer ispolymerizable.
 4. The process of claim 3, wherein the surfactant monomeris polymerized to 10-acrylamido decenoxy carbonyl-L-leucinate.